Chapter 2 Quadratics - Year 1 Flashcards
What so you do when you find a hidden quadratic?
You write it in terms of another letter.
You say that a letter is = to the x term with no power
You then solve the quadratic with your term
Then you substitute the x term back into the equation and solve for x
You should substitute your value back in to see if it is a real value or not
What is the domain of a function?
The set of possible inputs of a function
What is the range of a function?
The set of possible outputs of the function
How do you right x is a member of all real numbers?
That x is a member of all real numbers
What are the roots of an equation?
What are some other words for roots?
When f(x) = 0 (where the graph crosses the x axis)
The roots/zeros/solutions
What do you do when a question asks you to find all the values for which f(x)=g(x)
You put them equal to each other and solve
What do you do when a question asks you to find the roots of a function?
Put the function equal to 0
Solve the equation of the function
What do you do when a question asks you to determine the minimum value of a function?
You find the minimum value through completing the square or differentiation.
THE MINIMUM VALUE WILL BE THE Y VALUE
You then state that the minimum value is y and it occurs when x = …
What does sketch mean?
How do you do this if you are given a normal quadratic?
What values do you include?
You draw a rough diagram of it. It is not meant to be accurate.
You solve the equation to find the roots - this is where the graph will cross the x axis
If the x^2 is negative then it will be a sad quadratic
You should include the roots, turning point, where it crosses every axis.
Normally the question will tell you what it wants
How so you deduce the equation of a quadratic if you are given a sketch?
You are normally given the roots so you know the answers to the equation
You then reverse the sign on each root and write it in the for (x+a)(x+b)
You then expand the brackets.
You may be given y intercept
You know that the value without an x in your equation will be the y intercept so you need to work out what you need to multiply your equation by so that the y intercept match
Make sure to check if the quadratic is sad or happy so you know if you need to multiply for -1 or not
What is the discriminant?
If a quadratic has 2 roots what do we know about the discriminant?
b^2-4ac > 0
The discriminant is positive
If a quadratic has 1 roots what do we know about the discriminant?
b^2-4ac = 0
The discriminant is equal to 0
If a quadratic has no roots what do we know about the discriminant?
b^2-4ac < 0
The discriminant is negative
What phrase should make you think discriminant?
Equal roots
The discriminant will be 0
What should you do if you are given a quadratic equation with unknowns in it and told that it has either 2 roots, equal roots or no roots?
Right out the discriminant and state that it is equal to 0 (b^2-4ac = 0)
Then write a=, b= and c= down your page
You should wrote the corresponding values next to a,b and c (ax^2+bx+c)
Then substitute your values into your equation of b^2-4ac = 0
Solve the equation for the answer
What is the answer to a 1 mark question “what does the constant mean in this equation” in a quadratic?
The height of something (a tower)
How do you calculate how long an object was in the air for?
Put the equation =0
Solve the equation
Do either t-0 (if 1 value of t is negative)
Or
T2-T1
How do you find the maximum height of an object above the ground if it is modelled as a quadratic
Complete the square or differentiate
You can then find the turning point
A height of x at y seconds
When do you use U or N when using set notation?
If it is <0 it will always be 1 continues module
When it is >0 you will always have to use the or (u) sign with 2 different modules
Factorise this?
What can’t you do?
Why?
You can’t divide because you will loose a solution
How many solutions does x^5-5 have?
How do you know this?
1 real solution
The graoh of x^5 would only habe 1 real solution at the origin.
With the -5 you are just translating the graph 5 units to the right so there will only be 1 real solution
